If , and , find the value of…

MATHEMATICS · Subjective · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

x=\tan\frac{b-c}{2}\tan\frac{a}{2}

y=\tan\frac{a-b}{2}\tan\frac{c}{2}

and

z=\tan\frac{c-a}{2}\tan\frac{b}{2}

, find the value of

x+y+z+xyz